To obtain images of the subsurface, a seismic method is often used, which consists in creating and sending seismic waves in the ground using sources such as explosives or vibrator trucks on land, or airguns offshore. The seismic waves penetrate the ground and get bounced, or reflected off geological discontinuities in the subsurface. As a result, they come back to the surface, where they are recorded using arrays of three component geophones (on land), or hydrophones (offshore) which are regularly distributed to cover areas of several square kilometers.
Recent advances in seismic acquisition techniques have considerably improved the illumination of the subsurface. This capability to better compensate for uneven illumination represents a boon for production of new images of the subsurface. Seismic acquisitions are typically designed to be strongly redundant, in order to improve the signal to noise ratio; however, more data potentially means more diversity in the quality across different partitioned data. Wide azimuth acquisition may yield localized data areas that are “poor” in quality for certain azimuths, and will penalize the “good” data yielded in those locations on other azimuth cubes when processed into the final stack
Additionally, the inadequacy of the physics we use at various stages of the seismic processing workflow does not allow to fully benefit from all the new available measurements. Inaccuracy of the velocity models produces errors in the computed travel-times and these lead to inconsistencies in the positioning of seismic events in different pre-stack images; if not properly aligned before summation they can interfere destructively yielding to a defocused migrated image. Advancement in velocity estimation techniques will certainly lead to more adequate subsurface models over time, but a certain amount of inaccuracies in our velocity model is something we will likely always have to deal with.
The last years sparked a flurry of activity on various flavors of image enhancement through optimized summation of pre-stack migrated images. Most of them stem from the observation that conventional stacking is proficient only when all traces have similar amplitudes and S/N and when the noise patterns are statistically independent of the noise of any other trace and of the signal (Mayne, W. H., 1962, Common reflection point horizontal data stacking techniques: Geophysics, 27, 927-938, doi:10.1190/1.1439118; Neelamani, R., T. A. Dickens, and M. Deffenbaugh, 2006, Stack-and denoise: A new method to stack seismic datasets: 76th Annual International Meeting, SEG, Expanded Abstracts, 2827-2831; Robinson, J. C., 1970, Statistically optimal stacking of seismic data: Geophysics, 35, 436-446, doi:10.1190/1.1440105). The basic idea is to enhance the signal-to-noise ratio by only stacking those volumes that contain consistent and relevant information. Liu et al. (Liu, G., S. Fomel, L. Jin, and X. Chen, 2009, Stacking seismic data using local correlation: Geophysics, 74, no. 3, V43-48.) and Compton et al. (Compton, S., and C., Stork, 3D nonlinear stack enhancement: Correlation based stacking: SEG Technical Program Expanded Abstracts 2012: pp. 1-5) propose that weights represent a measure of the local correlation between each input trace and a conventional stacking reference trace. Kun et al. (Kun, J., X. Cheng, D., Sun, and D., Vigh, 2014, Migration imaging enhancement through optimized alignment of vector image partitions. SEG Technical Program Expanded Abstracts 2014: pp. 3699-3703. doi: 10.1190/segam2014-1648.1) apply a template matching technique between pre-stack images and a windowed reference image to find an optimal alignment and the weighting coefficients. These procedures are semi-automatic and the quality of the final stack is to some extent dependent on the quality of the reference trace. Local correlation stacking method can benefit from more advanced techniques to obtain the reference trace (Sanchis, C., and A. Hanssen, 2011, Enhanced local correlation stacking method: Geophysics, 76, no. 3, V33-45.).
FIG. 1 illustrates diagrammatically a survey of seismic data with a source S of seismic waves and at least one receivers G. It also shows a point B of the subsurface which is assumed to contribute to the signal sensed by one of the receivers G. The horizontal coordinates of point B of the subsurface are denoted by x, y (or only one spatial coordinate if 2D imaging instead of 3D imaging is considered), while its depth is denoted by z. FIG. 1 also provides a simplified representation (dashed lines 101 and 102) of the propagation of seismic waves from the source S to the point B and from the point B to the receiver G. The waves are refracted at discontinuities of the geological layers where the acoustic impedance changes, and reflected or diffracted at different positions including that of point B. In FIG. 1, a represents the aperture and m the common mid-point.
The data recorded in a seismic survey include, for each shot from a source S and for each receiver G, a seismic trace which is a time series of the signal sensed by the receiver G. The traces for a number of shots must be transformed to provide an image of the subsurface which will be the result of stacking or integrating a large amount of information. An important step of the transformation is the migration which consists in rearranging the data with respect to a model such that the stacking can be carried out coherently. The model is usually a map of the propagation velocity of the acoustic waves in the subsurface. It is not known a priori and it is a main challenge of all seismic imaging technologies to determine a model that will properly account for the field data after stacking.
In pre-stack depth migration (PSDM) methods, migrated data are computed for each shot using the velocity model and arranged in an output cube containing migrated values associated with positions in the subsurface. The cubes obtained for different shots are then analyzed to check consistency of the model: they can then be used either for obtaining a final image or producing Common Image Gathers. The model may be corrected and the process is iterated until a satisfactory image is obtained.
Common Image Gathers (CIGs) are popular tools for evaluating the migration velocity field and for imaging enhancement. They are made of data extracted from the output cubes, sorted in a convenient way for analysis so as to check the velocity model. A CIG is a bi-dimensional data structure defined for a given horizontal position x, y, with a first axis representing the depth z and a second axis representing a domain parameter A referred to for sorting the data of the output cubes. It contains reflectivity values obtained from the output cubes resulting from the migration, forming an image which can be analyzed to check and/or correct the velocity model. In this image, a pixel value at a point (z, A) represents a migrated value derived as a contribution of the subsurface position x, y, z to a seismic trace associated with the domain parameter A. Examples of commonly used domain parameters A include the aperture a, namely the distance between the center C of the source location and the receiver location G and the orthogonal projection of the point B on the surface.
The computation of common image gathers is not straightforward in all wavefield extrapolation methods.
Migration aperture is a critical parameter in Kirchhoff migration to obtain the best image quality from a given dataset. Optimal aperture selection is the result of a compromise. Reducing the migration aperture generally enhances the signal/noise ratio but to the detriment of dipping events imaging. Unfortunately, wave-equation migration methods have to deviate from this methodology.
However, such tools have been used mostly in migration methods based on estimation of travel times between reflectors and the surface. More sophisticated migration methods have been developed to build PSDM images by solving the wave equation so as to obtain more accurate reflector amplitudes and structural positioning. For example, reverse-time migration (RTM) is a two-way migration solution which can accurately describe wave propagation in complex media. It is increasingly used in seismic exploration by virtue of advances in computer power and programming.
The above-mentioned analysis tools are not used with wave equation PSDM methods, including RTM, because it is not known how to compute aperture indexed CIGs in these methods (mainly, the aperture indexed CIGs may only be computed, for now, in Kirchhoff method).
It would be desirable to obtain aperture indexed CIGs with different kinds of migration methods, in particular wave-equation methods including RTM or one-way migration methods, so as to keep the advantages of wavefield methods and, at the same time, address the limitation of the asymptotic assumption of ray-based methods, while sorting the migrated cubes in the same way as classical surface offset gathers.